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fix bug in general schur eigenvalues computation #30

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Dec 4, 2022
Merged

fix bug in general schur eigenvalues computation #30

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20 changes: 11 additions & 9 deletions src/schur.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -363,27 +363,29 @@ for (gges, elty) in ((:dgges_, :Float64),
end
chklapackerror(info[])
@inbounds for i in axes(A, 1)
ws.eigen_values[i] = complex(ws.αr[i], ws.αi[i])
ws.eigen_values[i] = complex(ws.αr[i], ws.αi[i])/ws.β[i]
end
return A, B, ws.eigen_values, ws.β, ws.vsl, ws.vsr
return A, B, complex.(ws.αr, ws.αi), ws.β, ws.vsl, ws.vsr
end
end
end

"""
gges!(ws, jobvsl, jobvsr, A, B; select=nothing, resize=true) -> (A, B, ws.eigen_values, ws.β, ws.vsl, ws.vsr)
gges!(ws, jobvsl, jobvsr, A, B; select=nothing, resize=true) -> (A, B, ws.α, ws.β, ws.vsl, ws.vsr)

Computes the generalized eigenvalues, generalized Schur form, left Schur
vectors (`jobsvl = V`), or right Schur vectors (`jobvsr = V`) of `A` and
`B`, using preallocated [`GeneralizedSchurWs`](@ref) workspace `ws`.
If `ws` is not of the right size, and `resize==true` it will be resized appropriately.

It is possible to specify `select`, a function used to sort the eigenvalues during the decomposition.
The function should have the signature `f(αr::T, αi::T, β::T) -> Bool`, where
`αr` and `αi` are the real and imaginary parts of the eigenvalue, `β` the factor, and `T == eltype(A).

The generalized eigenvalues are returned in `ws.eigen_values` and `ws.β`. The left Schur
vectors are returned in `ws.vsl` and the right Schur vectors are returned in `ws.vsr`.
It is possible to specify `select`, a function used to sort the eigenvalues to the top left corner of the Schur form.
The function should have the signature `f(αr::T, αi::T, β::T) -> Bool` where `T == eltype(A)`.
An eigenvalue `(αr[j]+αi[j])/β[j]` is selected if `f(αr[j],αi[j],β[j])` is true,
i.e. if either one of a complex conjugate pair of eigenvalues is selected,
then both complex eigenvalues are selected.
The generalized eigenvalues components are returned in `ws.α` and `ws.β` where `ws.α` is a complex vector and `ẁs.β`, a real vector.
The generalized eigenvalues (`ws.α./ws.β`) are returned in `ws.eigen_values`, a complex vector.
The left Schur vectors are returned in `ws.vsl` and the right Schur vectors are returned in `ws.vsr`.
"""
gges!(ws::GeneralizedSchurWs, jobvsl::AbstractChar, jobvsr::AbstractChar, A::AbstractMatrix,
B::AbstractMatrix)
20 changes: 12 additions & 8 deletions test/schur_test.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -53,24 +53,26 @@ end
B0 = randn(n, n)
ws = GeneralizedSchurWs(copy(A0))

A1, B1, eig1, β1, vsl1, vsr1 = LAPACK.gges!('V', 'V', copy(A0), copy(B0))
A2, B2, eig2, β2, vsl2, vsr2 = LAPACK.gges!(ws, 'V', 'V', copy(A0), copy(B0))
A1, B1, α1, β1, vsl1, vsr1 = LAPACK.gges!('V', 'V', copy(A0), copy(B0))
A2, B2, α2, β2, vsl2, vsr2 = LAPACK.gges!(ws, 'V', 'V', copy(A0), copy(B0))
@test isapprox(A1, A2)
@test isapprox(B1, B2)
@test isapprox(eig1, eig2)
@test isapprox(α1, α2)
@test isapprox(β1, β2)
@test isapprox(vsl1, vsl2)
@test isapprox(vsr1, vsr2)

# Using Workspace, factorize!
ws = Workspace(LAPACK.gges!, copy(A0))
A2, B2, eig2, β2, vsl2, vsr2 = factorize!(ws, 'V', 'V', copy(A0), copy(B0))
A2, B2, α2, β2, vsl2, vsr2 = factorize!(ws, 'V', 'V', copy(A0), copy(B0))
@test isapprox(A1, A2)
@test isapprox(B1, B2)
@test isapprox(eig1, eig2)
@test isapprox(α1, α2)
@test isapprox(β1, β2)
@test isapprox(vsl1, vsl2)
@test isapprox(vsr1, vsr2)
@test isapprox(sort(abs.(eigen(A0, B0).values)), sort(abs.(ws.eigen_values)))

show(devnull, "text/plain", ws)

for div in (-1,1)
Expand All @@ -91,14 +93,16 @@ end
0.86268 -0.212549 -0.211994]
ws = GeneralizedSchurWs(copy(A0))

A0, B0, eig, β, vsl, vsr = LAPACK.gges!(ws, 'V', 'V', copy(A0),
A0, B0, α, β, vsl, vsr = LAPACK.gges!(ws, 'V', 'V', copy(A0),
copy(B0);
select = (ar, ai, b) -> ar^2 + ai^2 <
FastLapackInterface.SCHUR_CRITERIUM *
b^2)
@test ws.sdim[] == 1
@test sign(real(eig[1])) == -1
@test sign(real(eig[2])) == 1
@test (real(α[1])/β[1])^2 < FastLapackInterface.SCHUR_CRITERIUM
@test (real(α[2])/β[2])^2 > FastLapackInterface.SCHUR_CRITERIUM
@test (real(α[3])/β[3])^2 > FastLapackInterface.SCHUR_CRITERIUM
@test isapprox(sort(abs.(eigen(A0, B0).values)), sort(abs.(ws.eigen_values)))
show(devnull, "text/plain", ws)
end
end